Question

triangle def is similar to triangle ghi. find the measure of side hi. figures are not drawn to scale.

Explanation:

Step1: Set up proportion

Since $\triangle DEF\sim\triangle GHI$, the ratios of corresponding - sides are equal. Let $EF = 11.3$, $DE = 8$, $GI = 48$, and $HI$ be the unknown side. The proportion is $\frac{EF}{HI}=\frac{DE}{GI}$.

Step2: Substitute values

Substitute the known values into the proportion: $\frac{11.3}{HI}=\frac{8}{48}$.

Step3: Cross - multiply

Cross - multiplying gives $8\times HI=11.3\times48$.

Step4: Solve for $HI$

First, calculate $11.3\times48 = 542.4$. Then, $HI=\frac{542.4}{8}=67.8$.

Answer:

$67.8$